User blog:Cheetahrock63/Cinioverses and Negative Two Dimensions
Trying out the weird idea of taking an AD concept and (attempting to) V&D-ify it. So, points—which are really just single locations—are called 0-dimensional. The empty set—the set that contains no elements and is the realization of the null polytope—is often considered "-1 dimensional". It doesn't literally ''have -1 dimensions, but it is an abstract polytope of rank -1 and rank corresponds with dimensionality for all other kinds of polytopes so it's somewhat helpful to think of null polytopes as "-1 dimensional". Naturally, one might wonder what a "-2 dimensional" polytope may be like. Back in the olden and blissful days of AD, that was exactly asked and so the birth of the Ciniovere (presumably originally a typo of "Cinioverse" that no one has bothered to really correct until Aarex tried but it was reverted back to "Ciniovere" three years later). No one really bothered to define what it meant for anything to be "-2 dimensional", leaving the -verse kinda ill-defined throughout its existence. Okay, so what would a -2 dimensional thing be like? Well, let's just start from something like 1D and take the necessary steps downward. The poset that a 1D line segment AB , as an abstract polytope, is a set consists of just four elements equipped with the necessary partial order: \emptyset , A , B , and AB . The poset that a 0D point A is a set consists of just two elements: A and \emptyset . The poset of a null polytope would be the set that contains the empty set. So going downwards from there, would that mean the poset of a "-2 dimensional shape" be just the empty set equipped with a partial order? I mean, yeah I guess? I'd probably think so. Okay so such a shape wouldn't actually be an abstract polytope since it breaks the property of needing to have a least and greatest subfacet (since it literally has no subfacets) but I don't think that really matters other than the fact that it crushed my hopes and dreams of calling it a "nuller polytope" or "dinull polytope". Now when realizing our -2 dimensional thingy, you don't end up with anything. Literally, you don't end up with anything. You get NOTHING! Like, you don't even get the empty set—a role filled by the nullitope. The poset that would give an indication as to what the shape would be like realized as contains nothing. So the -2 dimensional shape is literally nothing. So, I guess there is no -2 dimensional shape in that sense. At least, not any mathematical one. But thinking outside of math, one could say that the -2 dimensional thing ''is that nothingness. Like, you could say that -2D shape = Set-theoretical emptiness. And then, you could talk about it as if it were are -verse like how we do so with the empty set (nullverse). So I guess the Cinioverse could be talked about as set-theoretical emptiness but seen as a -verse. Huh. Neat. Now would the poset of a "-3 dimensional shape" be that set-theoretical emptiness equipped with a partial order? Sure. But I guess the contents of set-theoretical emptiness is still set-theoretical emptiness so maybe a "-n dimensional shape" for natural n bigger than 1 is exactly the same thing as a -2D shape. Does that mean the Cinioverse contains itself? Eh, maybe. Too lazy to think anymore. also this is probably the closest thing to anything remotely hypercosmological and it arguably isn't really something i came up with (i didn't make up the concept of "set theory emptiness" or the name "Ciniover(s)e" all i did was attach the name to the concept) i'll get since antibox so after finishing it, i'll probably abandon it and leave it to the wolves (up to you to decide who the wolves are) ---- The Cinioverse (or Ciniovere) is the -verse that embodies set-theoretical emptiness—similar to how the nullverse is a realization of the empty set or null polytope as a -verse or how a pointverse is a realization of a single location or a point as a -verse. Based on the description of the Cinioverse as "set-theoretical nothing", one might assume that it corresponds with the empty set. However, this is not true. While the empty set is empty, it is not emptiness or nothing. The empty set and null polytope are as much a thing as any other mathematical object. They just happen to be objects that contain nothing. Consequently, the nullverse is just a -verse that contains nothing. Said nothingness is what the Cinioverse is. The nullverse contains nothing while the Cinioverse is that nothing. The null polytope, the least subfacet of any given abstract polytope and the realization of the polytope that's the set containing the empty set equipped with a partial order, is an abstract polytopes of rank -1. Because rank corresponds to dimensionality for all other polytopes, it can be helpful to think of null polytope as having a dimension of -1. Going a step downwards, the empty set equipped with a partial order can be viewed as the poset of something with a "dimension of -2". Such an object will have no realization as a mathematical object as there are no contents of the empty set and it won't be an abstract polytope as there are no elements of the poset. The object, which would end up being whatever the contents of the empty set are, is set-theoretically nothing as there are no elements in the empty set. One way of interpreting this is to say that there is no such thing as a "-2 dimensional object" in that sense. Another way is to think of the nothingness as the "-2 dimensional object". Whatever is the case, said -2 dimensional object cannot be talked about as if it were a mathematical object and even if the Cinioverse was an object, the Nullverse may just be taken to be an object that just contains no mathematical objects to circumvent issues of it containing an object like the Cinioverse (or The Antibox). Relationship with the Nullverse Relationship with the Antibox Relationship with the Boxvoid Category:Blog posts